So, without further delay...
"Kaitou Kid's Busy Date" ("怪盗キッドの忙しいデート"/"Kaitou Kid no isogashii DEETO")
Note: Based on "Kaitou Kid's Busy Holiday" from Magic Kaito volume 1, chapter 4.
The episode opens up with a recap of the previous special...not much else to say except that the instrumental jazzy end tune from the first special (which I suppose we can say is the Magic Kaito main theme) returns during the recap. Nice, considering since this is a Conan broadcast on YTV, so we won't hear it again. (Unless Animax decides to air the Kid specials on their own again, outside of being forced to have Conan opening and ending themes.)
But hey, we still get all new music throughout the whole episode. WOOHOO! Kaito even managed to get his own "Conan title card" music cue. Instead of the usual score we get a jazz organ cue. Niiice.
Well this certainly wasn't in the original. Kaito threatens Jii with the card gun and demands to know why Toichi was the Kaitou Kid, stole jewels, and why he died. Jii stumbles over his words before glancing over at a picture of Chikage, Toichi, and a young Kaito. Kaito, following his gaze realizes whatever the reason Jii won't say anything must involve his mother somehow. (Hoo? Are we adding hints regarding a certain Phantom Lady, animation staff?) Kaito recalls that his mother on the video he saw in the first special that Chikage mentioned Kaito would probably become very busy very soon. Kaito gives up his line of questioning and figures he'll get the answers eventually by continuing to be Kid.
Believe it or not, the hang-glider cape is actually making an early appearance. Kid didn't start using it until volume 2, chapter 4. To be fair, I suppose the animation staff must feel the viewers have gotten so used to seeing Kid with it that'd it be jarring to see him use the odd mechanical devices and rocket-powered items he originally used in the early chapters.
This is where the actual chapter in Magic Kaito begins. The animation staff really have to do a lot of work adapting these Magic Kaito chapters. In the actual story, Kid's face is seen by Nakamori on page 3 as Kid is trying to steal the Angel Crown. He drops the crown and flees before Nakamori can catch him, but not before leaving a new warning message ON NAKAMORI'S BACK saying he'll return for the crown. In the animated version, Kid successfully steals the Angel Crown and is only seen by Nakamori when he tries making his escape off the rooftop using the glider (around 7 minutes into the episode). An odd wind caught him, so he was unable to get out of the light in time. This wind also causes Kid to fall quite ungracefully off the building, supposedly landing in a tree, and then fleeing via the sewer (ick) but not before leaving a new warning message saying he'll return for the crown.
Aoko's request for a date from Kaito goes as it does in the manga...oh hey there, Keiko! There was a pigtailed-girl in the original chapter, but given the lack of glasses, it might not have been Keiko, but this time around it's pretty obvious. The scene with Aoko and Ginzo goes the same as well.